Rectangle ABCD is shown in the figure. If ABCD is not a square, which of the following is a pair of perpendicular line segments?

Rationale

AB and BC are a pair of perpendicular line segments.

In rectangle ABCD, the sides AB and BC meet at point B, forming a right angle, which is characteristic of rectangles. This perpendicular relationship is crucial for establishing the right angles that define the rectangle's properties.

A (AB and DC) YOUR ANSWER

Both AB and DC are opposite sides of the rectangle. As such, they are parallel to each other and do not intersect at any angle, making them non-perpendicular. The definition of perpendicularity requires that two lines meet at a right angle, which is not the case here.

B (AD and BD) YOUR ANSWER

Line segment AD is a vertical side of the rectangle, while BD is a diagonal line connecting points B and D. Although AD forms a right angle with the base AB, it does not intersect BD at a right angle, as BD cuts across the rectangle. Thus, they are not perpendicular to each other.

C (AC and BD) YOUR ANSWER

AC is a diagonal line connecting points A and C, while BD is the diagonal connecting points B and D. Although each line segment connects opposite corners of the rectangle, they do not intersect at a right angle. Instead, they form angles that are not 90 degrees, which excludes them from being perpendicular.

D (AB and BC) CORRECT

AB is a horizontal side, and BC is a vertical side of the rectangle, meeting at point B. This intersection creates a right angle, fulfilling the requirement for perpendicularity. Thus, AB and BC are indeed perpendicular to each other.

Conclusion

In rectangle ABCD, the only pair of segments that are perpendicular to each other is AB and BC, which intersect at point B to form a right angle. The other choices involve segments that are either parallel or do not meet at a right angle, confirming that only AB and BC meet the criteria for perpendicular segments in this scenario.

Rectangle ABCD is shown in the figure. If ABCD is not a square, which of the following is a pair of perpendicular line segments?

AB and BC are a pair of perpendicular line segments.

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